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A college professor states that this year's entering students appear to be smarter than entering students from previous years. The college's records indicate that the mean IQ for entering students from earlier years. is 110.3. Suppose we want to sample a smaller number of this year's entering students and carry out a hypothesis test to see if the professor statement can be supported. State the null and alternative hypothesis.

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Answer:

[tex]H_{0}[/tex]: μ = 110.3

[tex]H_{a}[/tex]: μ > 110.3

Step-by-step explanation:

Let μ be the mean IQ of this year's entering students.

Then null and alternative hypotheses are:

  • [tex]H_{0}[/tex]: μ = 110.3 (this year's students mean IQ is at most the mean IQ of the entering students from previous years)
  • [tex]H_{a}[/tex]: μ > 110.3 (this year's students mean IQ is higher than the mean IQ of the entering students from previous years)

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